Coordonnées polaires sur les surfaces riemanniennes singulières
Troyanov, Marc
Annales de l'Institut Fourier, Tome 40 (1990), p. 913-937 / Harvested from Numdam
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Nous étudions les conditions sous lesquelles un point d’une surface riemannienne possède un voisinage pouvant être paramétrisé par des coordonnées polaires. Le point en question peut être un point régulier ou un point singulier conique. Nous étudions aussi la régularité de ces coordonnées polaires en fonction de la régularité de la courbure.

We study conditions under which a point of a Riemannian surface has a neighborhood that can be parametrized by polar coordinates. The point under investigation can be a regular point or a conical singularity. We also study the regularity of these polar coordinates in relation with the regularity of the curvature.

@article{AIF_1990__40_4_913_0,
     author = {Troyanov, Marc},
     title = {Coordonn\'ees polaires sur les surfaces riemanniennes singuli\`eres},
     journal = {Annales de l'Institut Fourier},
     volume = {40},
     year = {1990},
     pages = {913-937},
     doi = {10.5802/aif.1241},
     mrnumber = {92d:30029},
     zbl = {0711.53017},
     mrnumber = {1096597},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1990__40_4_913_0}
}

Troyanov, Marc. Coordonnées polaires sur les surfaces riemanniennes singulières. Annales de l'Institut Fourier, Tome 40 (1990) pp. 913-937. doi : 10.5802/aif.1241. http://gdmltest.u-ga.fr/item/AIF_1990__40_4_913_0/

[B] L. Bers, Local solution of General Linear Elliptic Equation, Comm. Pure Appl. Math., VIII (1955), 473-496. | MR 17,743a | Zbl 0066.08101

[F] H. Federer, Geometric Measure Theory, Springer, 1969. | MR 41 #1976 | Zbl 0176.00801

[GT] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equation of Second Order, Springer Verlag, New York, 1977. | MR 57 #13109 | Zbl 0361.35003

[H1] P. Hartman, On the local uniqueness of geodesics, Amer. Jour. Math., 72 (1950), 723-730. | MR 12,357b | Zbl 0039.16803

[H2] P. Hartman, Ordinary Differential Equations, second edition, Birkhaüser, 1982. | MR 83e:34002 | Zbl 0476.34002

[HT] D. Hulin et M. Troyanov, Prescribing curvature on open surfaces, preprint (1990). | Zbl 0799.53047

[HW] P. Hartman and A. Wintner, On the problem of geodesics in the small, Amer. Jour. Math., 73 (1951), 132-148. | MR 12,742e | Zbl 0042.15605

[LV] O. Lehto et K. Virtanen, Quasiconformal Mappings in the Plane, Springer Verlag, New York, 1973. | MR 49 #9202 | Zbl 0267.30016

[P] E. Picard, De l'intégration de l'équation Δu = eu sur une surface de Riemann fermée, Journal de Crelle, 130 (1905), 243-258. | JFM 37.0375.02

[T] M. Troyanov, Prescribing curvature on compact surfaces with conical singularities, Trans. A.M.S. (to appear). | Zbl 0724.53023